Math 583-1 Advanced Functional Analysis 4(3+1)
Spectrum of an operator, compact linear operators and their spectral properties, spectral properties of bounded self-adjoint operators, positive operators, product of positive operators, square root of positive operator, projection operators: Theorem (positivity, norm), Theorem (partial order), Theorem (product of projections), Theorem ( sum of projections), Theorem (difference of projections), Spectral family of a bounded self-adjoint operator, Banach algebras, Gelfand’ mapping, spectral theorem for normal operators.
1. E. Kreyszig, "Introductory Functional analysis with Applications", John Wiley & sons, 1978.
2. K. Zhu, An Introduction to Operator Algebras, CRC Press, 1993.
3. I. Gohberg and S. Goldberg, Basic Operator Theory, Birkhauser, 1980.
4. W. Rudin, "Functional Analysis", McGraw-Hill, Inc., 1991.
5. C. Swarz, "An Introduction to Functional Analysis", Marcel Dekker, 1992.
6. Taylor and D. C. Lay, "Introduction to Functional Analysis", John Wiley & sons, 1980.